It is known from E. D. Donets, USSR Inventor's Certificate No. 248860, Mar. 16, 1967; Bull. OIPOTZ 23, 65 (1969) that there is the electron-beam method for the production of highly charged ions in the trap formed by the electron beam of a constant radius propagating inside the drift tube, which consists of, at least, three sections with positive potentials applied at the edge sections with respect to the middle one. The control of axial movement of ions (injection, trapping and extraction of ions from the trap) is carried out by variation of the potential distribution on sections of the drift tube.
The axially symmetric magnetic field is used for focusing the electrons emitted from cathode of the electron gun into the electron beam of consistent diameter and of relatively large length. In this case, the current density of the electron beam, which determines the maximum achievable ion charge and the average ion beam current, cannot exceed of the so-called Brillouin electron current density. In real running electron beam ion sources, the current density turns out to be less than Brillouin limit by many times.
It is also known from M. Kleinod, R. Becker, O. Kester, A. Lakatos, H. Thomaae, B. Zipfel, and H. Klein, Frankfurt EBIS development: fundamental research and new applications, Rev. Sci. Instrum. 65, 1069 (1994) that there is the method for the production of highly charged ions in crossover of the electron beam, which is focused by the system of electrostatic lenses. The drawbacks of this method are the aberrations of lenses and the need of high voltages, which result in relatively low current density.
It is well known that the electron beam, which is formed in electron gun with cathode placed in the zero magnetic field, is transformed into the sequence of optical focuses in the axially symmetric magnetic field of sufficient length (thick magnetic lens). Theoretically, the first (main) focus is the most acute. In the main magnetic focus, the electron beam reaches the current density, which is considerably greater than that in the case of the Brillouin flow.
In subsequent optical focuses, the current density of electrons drops with length of the beam due to influence of the thermal velocities of electrons and effects of aberrations of the electrostatic (anode of the electron gun) and magnetic (focusing magnetic field) lenses. This is described in K. Amboss, Studies of a Magnetically Compressed Electron Beam, IEEE Trans. Electr. Devices 16, 897 (1969).